A352520 Number of integer compositions y of n with exactly one nonfixed point y(i) != i.

0, 0, 2, 1, 4, 5, 3, 7, 8, 9, 6, 11, 12, 13, 14, 10, 16, 17, 18, 19, 20, 15, 22, 23, 24, 25, 26, 27, 21, 29, 30, 31, 32, 33, 34, 35, 28, 37, 38, 39, 40, 41, 42, 43, 44, 36, 46, 47, 48, 49, 50, 51, 52, 53, 54, 45, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 55, 67

Offset: 0

Author

Gus Wiseman, Mar 29 2022

Keywords

• nonn

Examples

			The a(2) = 2 through a(8) = 8 compositions:
  (2)    (3)  (4)      (5)      (6)    (7)        (8)
  (1,1)       (1,3)    (1,4)    (1,5)  (1,6)      (1,7)
              (2,2)    (3,2)    (4,2)  (5,2)      (6,2)
              (1,2,1)  (1,1,3)         (1,2,4)    (1,2,5)
                       (1,2,2)         (1,3,3)    (1,4,3)
                                       (2,2,3)    (3,2,3)
                                       (1,2,3,1)  (1,2,1,4)
                                                  (1,2,3,2)
		

Crossrefs

Compositions with no nonfixed points are counted by A010054.

The version for weak excedances is A177510.

Compositions with no fixed points are counted by A238351.

The version for fixed points is A240736.

This is column k = 1 of A352523.

A011782 counts compositions.

A238349 counts compositions by fixed points, rank stat A352512.

A352486 gives the nonfixed points of A122111, counted by A330644.

A352513 counts nonfixed points in standard compositions.

Cf. A008930, A088218, A098825, A114088, A115994, A219282, A238352, A238874, A350839.

Programs

Mathematica

pnq[y_]:=Length[Select[Range[Length[y]],#!=y[[#]]&]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],pnq[#]==1&]],{n,0,15}]

Extensions

More terms from Alois P. Heinz, Mar 30 2022